Abstract
In this chapter we present results on performance limitations in linear single-input single-output control systems. These results are the cornerstones of classical design. We focus on the sensitivity and complementary sensitivity functions, S and T. Although this chapter is based on contributions by many authors, mainly during the 80’s, they may be seen with justice as direct descendants of the many ideas contained in Bode (1945).
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Notes and References
Bode Integral Formulae
§3.1.1 is taken mainly from Bode (1945); §3.1.2 is based on results of Horowitz (1963), Freudenberg & Looze (1985,1987), Middleton & Goodwin (1990) and Middleton (1991). §3.1.3 follows Freudenberg & Looze (1988), but it is also possible to obtain similar results assuming functional bounds, as was done in Middleton (1991).
The Water-Bed Effect
This result was first discussed by Francis & Zames (1984), and then revisited by Freudenberg & Looze (1987) and Doyle et al. (1992). The result presented here is the one given in Francis & Zames (1984).
Poisson Integral Formulae
This section is largely taken from Freudenberg & Looze (1985, 1988). For an interesting discussion on the complementarity of S and T see Kwakernaak (1995).
Discrete Systems
§3.4 is based on Sung & Hara (1988). A unification of both continuous and discrete-time results has been made in Middleton (1991), where the Bode integral for T is also derived.
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© 1997 Springer-Verlag London Limited
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Seron, M.M., Braslavsky, J.H., Goodwin, G.C. (1997). SISO Control. In: Fundamental Limitations in Filtering and Control. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0965-5_3
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DOI: https://doi.org/10.1007/978-1-4471-0965-5_3
Publisher Name: Springer, London
Print ISBN: 978-1-4471-1244-0
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